We will assume that \(X\)  is randomized by simple random sampling within each village, inducing propensity classes that were the interaction of village and number of first round friends. In fact, [1]} reports that treatments were stratified by family size and amount of land used for rice farming; however, further details are not included, and additionally these variables are missing for a significant fraction of the first round units. For this reason, our results for this example should be viewed primarily as a illustration of the proposed method.
